For some reason I am unable to buy dog food by clicking on the sticky note. It acts like a broken button. I did not have this problem when I had a cat in a previous game. Any ideas on how to fix this?
I think you can shop only on somedays. Not all.
Maybe like weekends.
Then that would mean the cat food is bugged. I could buy cat food any time I got the sticky tab and it did not take an activity from me or anything. I actually thought it was good because that meant I could shop for free and whenever my cat was hungry. 
Can anyone else confirm this?
If you had a laptop at the same time as the cat then you can shop anytime. I think the sticky’s do have a bug that allows you to shop without using an activity.
Do you have a car? And if you don’t have one now, did you have one in the game where you had a cat? The shopping center is evidently too far to walk to it in the evening, so if you travel by foot, you can only go there on the weekends. If you have a car, your options expand.